An Interesting Dinner with Pi

piToday is Pi Day (3.14.15).  Pi is not a person.  But it is very interesting.

The people who initiated the hunt for pi were the Babylonians and Egyptians, nearly 4000 years ago. They found that pi was slightly greater than 3, and came up with the value 3 1/8 or 3.125.  At around 1650 BC, a scribe named Ahmes implied in the Rhind Papyrus that pi = 4(8/9)2 = 3.16049, which is also fairly accurate. The next approximation of pi is found in the Old Testament. 1 Kings 7:23, says: “Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.” This implies that pi = 3.

The first man to really make an impact in the calculation of pi was the Greek, Archimedes of Syracuse. Archimedes fapproximated the circle’s circumference instead of the area. He started with an inscribed and a circumscribed hexagon, then doubled the sides four times to finish with two 96-sided polygons. The earliest value of pi used in China was 3. In 263 AD, Liu Hui arrived at the value pi = 3.14159, which are the correct first five digits. Near the end of the 5th century, Tsu Ch’ung-chih and his son Tsu Keng-chih calculated 3.1415926 < pi < 3.1415927. Soon after, the Hindu mathematician Aryabhata gave the ‘accurate’ value 62,832/20,000 = 3.141.  Another Indian mathematician, Brahmagupta, calculated pi would approach the square root of 10 [=3.162…].

In 1593, Adrianus Romanus used a circumscribed polygon with 230 sides to compute pi to 17 digits after the decimal, of which 15 were correct. Just three years later, Ludolph Van Ceulen presented 20 digits, and by the time he died in 1610, he had accurately found 35 digits.  These digits were cut into his tombstone in St. Peter’s Churchyard in Leyden. In 1873, an Englishman named William Shanks used the formula to calculate 707 places of pi, but only the first 527 digits were correct. Johann Heinrich Lambert proved the irrationality of pi first in 1761 and then in more detail in 1767. In 1882, Ferdinand von Lindemann proved the transcendence of pi. Since this means that pi is not a solution of any algebraic equation, it lay to rest the uncertainty about squaring the circle.

In the twentieth century, computers allowed mathematicians to get to previously incomprehensible results. In 1947, D. F. presented 808 digits of pi. One and a half years later, Levi Smith and John Wrench hit the 1000-digit-mark . Finally, in 1949, the ENIAC (Electronic Numerical Integrator and Computer) was finally functional, the gigantic machine calculated 2037 digits in just seventy hours. John Wrench and Daniel Shanks found 100,000 digits in 1961, and the one-million-mark was surpassed in 1973.

Just thirty-nine decimal places would be enough to compute the circumference of a circle surrounding the known universe to within the radius of a hydrogen atom. At the present time, the only tangible application for all those digits is to test computers and computer chips for bugs.

March 14th has long been considered to be “pi” day, celebrated by eating pies (and maybe doing some Math.  There are some wild and hardcore partiers out there).  This is my favorite recipe, by Rose Levy Beranbaum, from her book The Baking Bible.  Her other book, The Bread Bible, is my favorite cookbook of all time.  We’re talking serious breads, scones, cakes.  But here is the- dare I say- perfect pie recipe:

(this recipe also holds a special place in my heart because my husband made it on the 4th of July last year- just hours before my water broke and we headed to the hospital to give birth to my own little sweetie pie).

Oven Temperature: 425°F/220°C

Baking Time: 45 to 55 minutes

Special Equipment: One 9 inch pie plate | An expandable flan ring or 12-inch round cardboard template | A baking stone or baking sheet | A foil ring to protect the edges of the crust

Ingredients for the dough:

12 tablespoons (1½ sticks) of cold, unsalted butter (6 ounces or 170 grams)
2-1/2 cups plus 1 tablespoon (or 2⅓ cups plus 1 tablespoon) pastry flour (or bleached all-purpose flour), lightly spooned into the cup and leveled off (10.2 ounces or 290 grams)
1/2 teaspoon fine sea salt (3 grams)
1/4 teaspoon baking powder; use only an aluminum-free variety (1.1 grams)
1/2 cup cold cream cheese (4.5 ounces or 128 grams)
3 tablespoons heavy cream (44 ml, 1.5 ounces or 43 grams)
1 tablespoon cider vinegar (15 ml)

Ingredients for the filling:

About 6 medium baking apples (2 1/2 pounds/1,134 grams) (8 cups sliced or 2 pounds sliced or 907 grams sliced)
1 tablespoon lemon juice, freshly squeezed (15 ml or 0.6 ounce or 16 grams)
1/4 cup firmly packed light brown Muscovado sugar, or dark brown sugar (1.9 ounces or 54 grams)
1/4 cup granulated sugar (1.8 ounces or 50 grams)
1/2 to 1-1/2 teaspoon ground cinnamon (1.1 to 3.3 grams)
1/4 teaspoon nutmeg, freshly grated
1/4 teaspoon fine sea salt
1/2 cup unpasteurized apple cider, unsweetened (118 ml or 4.3 ounces or 122 grams )
1/2 tablespoon cornstarch (for the apple cider) (5 grams)
2 tablespoons unsalted butter (1 ounce or 28 grams)
1 tablespoon plus 1 teaspoon cornstarch (for the apples) (12 grams)

  1. To make the dough in the food processor, cut the butter into small (about ½ inch) cubes.
  2. Wrap it in plastic wrap and freeze it until frozen solid, at least 30 minutes.
  3. In a gallon-size reclosable freezer bag, place the flour, salt, and baking powder and freeze for at least 30 minutes. In the food processor, place the flour mixture. Cut the cream cheese into 3 or 4 pieces and add it to the flour. Process for about 20 seconds, or until the mixture resembles coarse meal. Add the frozen butter cubes and pulse until none of the cubes is larger than the size of peas. (Toss with a fork to see the size better.) Remove the cover and add the cream and vinegar. Pulse until most of the butter is reduced to the size of small peas. The mixture will be in particles and will not hold together. Spoon it into the plastic bag or, wearing latex gloves (which help to prevent sticking), empty it onto the counter. (For a double crust pie, it is easiest to divide the mixture in half. Spoon one-half into the bag, knead as described below, and then repeat with the second half. Hold either side of the bag opening and alternate using the heel of your hand and your knuckles to knead and press the mixture, from the outside of the bag, until most of the mixture holds together in one piece. Cut open the bag and empty the dough onto a large sheet of plastic wrap. Use the plastic wrap to finish kneading together the dough just until it feels slightly stretchy when pulled. (If using latex gloves, use the heel of your hand to push and flatten the dough against the counter.) In a gallon-size reclosable freezer bag, place the flour, salt, and baking powder and freeze for at least 30 minutes. In the food processor, place the flour mixture. Cut the cream cheese into 3 or 4 pieces and add it to the flour. Process for about 20 seconds, or until the mixture resembles coarse meal. Add the frozen butter cubes and pulse until none of the cubes is larger than the size of peas. (Toss with a fork to see the size better.) Remove the cover and add the cream and vinegar. Pulse until most of the butter is reduced to the size of small peas. The mixture will be in particles and will not hold together. Spoon it into the plastic bag or, wearing latex gloves (which help to prevent sticking), empty it onto the counter. (For a double crust pie, it is easiest to divide the mixture in half. Spoon one-half into the bag, knead as described below, and then repeat with the second half.)
  4. Hold either side of the bag opening and alternate using the heel of your hand and your knuckles to knead and press the mixture, from the outside of the bag, until most of the mixture holds together in one piece. Cut open the bag and empty the dough onto a large sheet of plastic wrap. Use the plastic wrap to finish kneading together the dough just until it feels slightly stretchy when pulled. (If using latex gloves, use the heel of your hand to push and flatten the dough against the counter.)
  5. For a pie shell and standard 10 strip lattice, divide the dough into two-thirds and one-third. Use about 9.5 ounces/269 grams for the shell and the rest for the lattice, flattening the smaller part into a rectangle. Wrap each piece and refrigerate for 45 minutes or up to 2 days.
  6. For a double crust or 14 strip lattice pie, divide the dough into 2 equal pieces, about 11 ounces/312 grams each. Wrap each piece and refrigerate for 45 minutes or up to 2 days.
  7. For an extra flaky pie crust approaching puff pastry but more tender, roll the dough into a rectangle and give it a business letter fold (fold it into thirds). Roll it again to flatten it and make it a fairly even square. Wrap the dough, flatten it into a disc (or 2 discs for a double crust or lattice pie), and refrigerate for 45 minutes or up to 2 days.
  8. To make the dough by hand, place a medium mixing bowl in the freezer to chill. Cut the butter into small (about ½ inch) cubes. Wrap it in plastic wrap and refrigerate for at least 30 minutes.
  9. Place the flour, salt, and baking powder in a medium bowl and whisk to combine. Add the cream cheese and rub the mixture between your fingers to blend the cream cheese into the flour until it resembles coarse meal. Spoon the mixture, together with the cold butter, into a gallon-size reclosable freezer bag. Express any air from the bag and close it. Use a rolling pin to flatten the butter into thin flakes. Place the bag in the freezer for at least 10 minutes, or until the butter is very firm. Transfer the mixture to the chilled bowl, scraping the sides of the bag. Set the bag aside. Sprinkle the mixture with the cream and vinegar, tossing lightly with a silicone spatula. Spoon the mixture back into the plastic bag. (For a double crust pie, it is easiest to divide the mixture in half. Spoon one-half into the bag, knead as described below, and then repeat with the second half.)
  10. Hold either side of the bag opening and alternate using the heel of your hand and your knuckles to knead and press the mixture, from the outside of the bag, until it holds together in one piece and feels slightly stretchy when pulled.
  11. For a pie shell and 10 strip lattice, divide the dough into two-thirds and one-third. Use about 9.5 ounces/269 grams for the shell and the rest for the lattice, flattening the smaller part into a rectangle. Wrap each piece and refrigerate for 45 minutes or up to 2 days.
  12. For a double crust or 14 strip lattice pie, divide the dough into 2 equal pieces. Wrap each piece and refrigerate for 45 minutes or up to 2 days. Store refrigerated, up to 2 days; frozen, 3 months.
  13. Remove the dough for the bottom crust from the refrigerator. If necessary, let it sit for about 10 minutes, or until it is malleable enough to roll.
  14. On a floured pastry cloth, pastry mat, or between two sheets of lightly floured plastic wrap, roll the dough into a ⅛ inch thick disc, 12 inches in diameter or large enough to line the bottom of the pie plate and extend slightly past the edge of the rim. Lift the dough from time to time and add flour as necessary to keep it from sticking. Before measuring the dough, make sure to lift it from the surface to allow it to shrink in so that it doesn’t retract when set in the pie plate. Use the expandable flan ring, or a small sharp knife with the cardboard template as a guide, to cut a 12 inch disc of dough.
  15. Transfer the dough to the pie plate, easing it into place. If necessary, trim the edge almost even with the edge of the plate. Cover with plastic wrap and refrigerate for a minimum of 30 minutes or up to 3 hours.
  16. The dough can be stored refrigerated, up to 2 days; frozen, 3 months.
  17. To prepare the apples, peel them and slice them in half. Use a melon baller to remove the cores and a small sharp knife to cut away any remaining peel. Slice the apples ¼ inch thick. Weigh or measure the apple slices and toss them with the lemon juice.
  18. In a large bowl, mix together the brown sugar, granulated sugar, cinnamon, nutmeg, and salt. Add the apples and toss to coat them with the sugar mixture. Let the apples macerate at room temperature for a minimum of 30 minutes or up to 3 hours.
  19. In a small saucepan, stir together the apple cider and the ½ tablespoon of cornstarch. Bring the mixture to a boil, stirring constantly. It will become very thick. Scrape it into a small bowl, cover tightly, and set it aside.
  20. Transfer the apples and their juices to a colander suspended over a bowl to capture the liquid. The mixture will release at least ½ cup/118 ml/5 ounces/142 grams of liquid.
  21. Transfer this liquid to a 4 cup microwavable measure with a spout that has been lightly coated with nonstick cooking spray. Add the butter and microwave for about 6 to 7 minutes until reduced to about ⅓ cup/79 ml/3.1 ounces/88 grams—or a little more if you started with more than ½ cup of liquid. It will be syrupy and lightly caramelized. Watch carefully to prevent burning. Alternatively, reduce the liquid in a saucepan, preferably nonstick, over medium-high heat. Swirl but do not stir it.
  22. Transfer the apples to a large bowl and toss them with the 1 tablespoon plus 1 teaspoon of cornstarch until all traces of it have disappeared. Pour the reduced syrup over the apples, tossing gently. (Do not be concerned if the syrup hardens on contact with the apples; it will dissolve during baking.) Scrape in the thickened apple cider and again toss gently to mix it in. Spoon the apples into the dough-lined pie plate. Moisten the border of the bottom crust by brushing it lightly with water.
  23. Roll out the dough for the top crust large enough to cut a 12 inch disc. Use the expandable flan ring, or a sharp knife with the cardboard template as a guide, to cut the disc of dough.
  24. Place the top crust over the apple filling. Tuck the overhang under the bottom crust border and press down all around the top to seal it. Crimp the border using your forefinger and thumb or a fork, and use a small sharp knife to make 5 evenly spaced 2-inch slashes in the top crust, starting about 1 inch from the center and radiating toward the edge. Cover the pie loosely with plastic wrap and refrigerate it for 1 hour before baking to chill and relax the dough. This will maintain flakiness and help to keep the crust from shrinking.
  25. Forty-five minutes or longer before baking, set an oven rack at the lowest level and place the baking stone or baking sheet on it. Place a large sheet of nonstick aluminum foil or foil lightly coated with nonstick cooking spray on top of the stone to catch any juices. Preheat the oven to 425°F/220°C.
  26. Place the foil ring on top of the pie to protect the edges from overbrowning and set the pie on the foil-topped baking stone. Bake for 20 minutes. For even baking, rotate the pie halfway around. Continue baking for 25 to 35 minutes, or until the juices bubble through the slashes and the apples feel tender but not mushy when a cake tester or small sharp knife is inserted through a slash.
  27. Cool on a wire rack for at least 4 hours before cutting. Serve warm or at room temperature.
  28. Room temperature, 2 days; refrigerated, 4 days.
  29. It’s fine to combine three or four kinds of apples, but be sure to choose apples with a low water content. Some of my favorites are Macoun, Cortland, Jonathan, Stayman Winesap, Rhode Island Greening, Golden Delicious, York Imperial, Northern Spy, Newtown Pippin, Idared, Pink Lady, and Granny Smith.
  30. If the apples are very tart, add up to 1/4 cup/1.8 ounces/50 grams more sugar. If using a very strong specialty cinnamon, use 1/4 to 3/4 teaspoons, depending on how much of a cinnamon flavor you want to give to the apples.

Happy pi day!

Source: The History of Pi by David Wilson

Source: Real Baking with Rose Levy Berenbaum

Source: The Bread Bible

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